T. every other element of A. Such a set is nite and triangular : no pair of di erential polynomials in A have the same leader. t. t. any element of A. Let A be an auto-reduced set. t. 9 . t. A satisfying 1. When A is an auto-reduced set of FfY g, we will note mathbfhA the product of all initials and separants of the di erential polynomial in A. Characteristic sets A ranking on FfY g induces a pre-order on the set of all auto-reduced subsets of FfY g. Let A = a1 ; : : : ; ar and B = b1 ; : : : ; bs be two auto-reduced subsets.